CMBR constraints on $R^2$ gravity

Considering the inflation model based on a $f(R)$ gravity theory, we obtain several important constraints from the large angular scale CMBR observations. First, the ordinary slow-roll assumption during the inflation together with Harrison-Zel'dovich spectral conditions chooses $R^2$ gravity as a unique candidate. Second, the $R^2$ gravity leads to specific near scale-invariant Harrison-Zel'dovich spectra both for the scalar and the tensor perturbations. Third, using the COBE-DMR data we derive the strong constraints on the coupling constant and the energy scale during the inflation. Also, our result shows the gravitational wave contribution to the CMBR anisotropy is negligible. So, the future observation can provide the strong constraints on the inflation model based on $R^2$ gravity. This is a summary of a talk presented in COSMO-01, and the more completed published version can be found in astro-ph/0102423.